𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A steady-state system in non-equilibrium thermodynamics including thermal and electrical effects

✍ Scribed by Pierre Degond; Stéphane Génieys; Ansgar Jüngel

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
147 KB
Volume
21
Category
Article
ISSN
0170-4214

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✦ Synopsis

Communicated by H. Neunzert

The steady-state equations for a charged gas or fluid consisting of several components, exposed to an electric field, are considered. These equations form a system of strongly coupled, quasilinear elliptic equations which in some situations can be derived from the Boltzmann equation. The model uses the duality between the thermodynamic fluxes and the thermodynamic forces. Physically motivated mixed Dirichlet-Neumann boundary conditions are prescribed. The existence of generalized solutions is proven. The key of the proof is a transformation of the problem by using the entropic variables, or electro-chemical potentials, which symmetrize the equations. The uniqueness of weak solutions is shown under the assumption that the boundary data are not far from the thermal equilibrium. A general uniqueness result cannot be expected for physical reasons. 1998 B. G. Teubner Stuttgart-John Wiley & Sons, Ltd.

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